Results for Exercise I-3 with COBAYA:
Analysis of the peaking power factors
E. Castro, S. Sánchez-Cervera, N. García-Herranz, D. Cuervo
[email protected]
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Background
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Objectives
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Methodology
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Results of k
eff•
Results of power distributions
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Results of peaking power factors
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Conclusions
Background
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UPM methodology for Uncertainty Quantification is based in two tools:• SCALE 6.2.1: NEWT and Sampler.
• COBAYA: core simulator with nodal and pin-by-pin capabilities
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Random few-group libraries for COBAYA can be generated in anautomatic way using SCALE by stochastic sampling of nuclear data with Sampler(NEWT) → presented in UAM-9
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UQ capabilities in COBAYA → presented in UAM-9• 1st. Order PT (full covariance matrix required)
• Sampled-based (set of random few-group libraries required)
Objectives
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Exercise I-3: UQ in TMI-1 full core calculations usingSCALE(NEWT)/COBAYA at both nodal and pin-by-pin levels
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Specific objectives:• Contribute with updated results to Ex I-3, computing uncertainties in
k-eff, radial power distributions and peak factors.
• Compare nodal and pin-by-pin results.
• Evaluate the probability distribution of core parameters.
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TMI-1 ARI core definition: FA Enrichment(w/o) BP(%) Gd (pins)1 4.00 -
-2 4.95 3.5 4
3 5.00 - 4
4 4.40 -
-5 5.00 3.5 4
6 4.85 - 4
7 4.95 - 4
8 5.00 - 8
9 4.95 - 8
10 4.95 3.5
-Methodology
SAMPLER / NEWT FA 1
SAMPLER / NEWT FA 2
...
SAMPLER / NEWT FA 27
Perturbed NEMTAB cross section libraries Perturbed COBAYA simulations Perturbed core results NEWT2NEMTAB tool
A sampling-based approach using SCALE and COBAYA was used to
propagate uncertainties in nuclear data to core parameters.
Advantages:
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Very easy to implement.
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Any kind of observable can be analyzed.
Methodology
SAMPLER / NEWT FA 1
SAMPLER / NEWT FA 2
...
SAMPLER / NEWT FA 27
Perturbed NEMTAB cross section libraries Perturbed COBAYA simulations Perturbed core results NEWT2NEMTAB tool
NEWT (SCALE 6.2.1) was used as lattice code.
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SAMPLER was used to produce perturbed NEWT inputs.
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56g-v7.1 cross sections and covariance library.
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11 unrodded FA, 7 rodded FA, 1 reflector.
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900 random samples for each fuel assembly type:
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900 * 19 lattice calculations.
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Nodal homogenization.
Methodology
SAMPLER / NEWT FA 1
SAMPLER / NEWT FA 2
...
SAMPLER / NEWT FA 27
Perturbed NEMTAB cross section libraries Perturbed COBAYA simulations Perturbed core results NEWT2NEMTAB tool
NEWT outputs are grouped together in NEMTAB-formatted libraries:
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NEWT2NEMTAB tool.
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Parametrized libraries as a function of coolant density, coolant
temperature, fuel temperature and boron concentration.
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Nodal library contains 19 materials.
Methodology
SAMPLER / NEWT FA 1
SAMPLER / NEWT FA 2
...
SAMPLER / NEWT FA 27
Perturbed NEMTAB cross section libraries Perturbed COBAYA simulations Perturbed core results NEWT2NEMTAB tool
COBAYA core simulator:
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Solves the multigroup neutron diffusion equation corrected by
interface discontinuity factors.
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Nodal solver: Analytic Coarse-Mesh Finit-Difference (ACMFD).
Methodology
SAMPLER / NEWT FA 1
SAMPLER / NEWT FA 2
...
SAMPLER / NEWT FA 27
Perturbed NEMTAB cross section libraries Perturbed COBAYA simulations Perturbed core results NEWT2NEMTAB tool
A statistical analysis of the 900 core results is performed:
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Mean values.
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Standard deviations.
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Moments of higher order.
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Histograms.
Results of k
effk
eff∆k/k(%)
Nodal
1.00373
0.515
Pin-by-pin
1.00350
0.515
Good agreement between the two solvers.
Results of k
effWith 200 samples: 62 pcm difference between the mean and the unperturbed values
Unperturbed (nominal)
value in blue Final relative SD
value in blue
Results of peaking power factors
Nodal
Pin-by-pin
F
∆Hnode/pin
1.71 (2.1%)
1.91 (2.8%)
F
∆Hassembly
1.64 (0.4%)
1.60 (1.1%)
F
xynode/pin
2.11 (0.5%)
2.46 (0.7%)
F
xyassembly
2.05 (0.5%)
2.12 (0.5%)
F
qnode/pin
2.56 (2.3%)
2.74 (2.7%)
F
qassembly
2.45 (0.5%)
2.30 (1.1%)
• Assembly averaged results can be used to compare both solvers.
• Mean values are consistent between solvers.
• Standard deviations show large differences.
• Are they normally distributed?
𝐹𝐹∆𝐻𝐻 = 𝑃𝑃𝑚𝑚𝑚𝑚𝑚𝑚�𝑃𝑃
𝐹𝐹𝑚𝑚𝑥𝑥 = 𝑚𝑚𝑚𝑚𝑚𝑚 𝑃𝑃𝐷𝐷𝑃𝑃𝐷𝐷(𝑧𝑧()𝑧𝑧𝑚𝑚𝑚𝑚𝑚𝑚)
𝐹𝐹𝑞𝑞 = 𝑃𝑃𝐷𝐷𝑚𝑚𝑚𝑚𝑚𝑚 𝑃𝑃𝐷𝐷
Results of peaking power factors
Pin-by-pin solver yields non-normal peaking factors, in contrast to the nodal solution.
Peaking factors uncertainty seems very sensitive to spatial meshing.
Results of peaking power factors
Pin peaking factors
Again, pin peaking power factors show non-normal distributions.
This implies that providing a mean value and a standard deviation is not enough to properly describe the uncertainty.
Results of peaking power factors
Hottest fuel assembly position in PBP simulations:
• Position A: 77 % of the random samples. • Position B: 23 % of the random samples.
Focusing on the assembly-averaged F∆H obtained using the pin-by-pin solver. F∆H = Normalized power of the hottest fuel assembly.
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SCALE/COBAYA is a suitable tool for UQ at both nodal and pin levels.It has been applied to Exercise I-3 / TMI-1
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Uncertainties in keff•
Consistent values between nodal and pin-by-pin simulations (∆k ≈ 500 pcm)•
Normally distributed results -> confirms that the mean value and the standarddeviation permit establishing confidence intervals
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A large number of simulations mandatory to obtain a mean value in perfectagreement with the nominal value.
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Uncertainties in peaking power factors•
The spatial mesh impacts the assembly-averaged peaking factors.•
Values computed with the pin solver (both pin- and assembly-averaged) do notfollow a normal distribution -> mean value and the standard deviation are not sufficient and their PDF are mandatory to construct the confidence intervals required for safety analysis.
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This behavior highlights the need of performing full core calculationsat the pin-level to get reliable estimates of the uncertainties in peaking factors.
